Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
n = int(input())
m = 2*n+0.5
l = int(n**(1/2))
flag = 0
for i in range(1,l+1):
    a = (m-((i+0.5)**(2)))**(1/2)-0.5 
    if a == int((m-((i+0.5)**(2)))**(1/2)-0.5) and a != 0:
        print("Yes")
        flag = 1
        break
    i = i+1
if flag == 0:
    print("No")